Simplify the following expression: $ p = \dfrac{-1}{4} - \dfrac{-1}{q - 1} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{q - 1}{q - 1}$ $ \dfrac{-1}{4} \times \dfrac{q - 1}{q - 1} = \dfrac{-q + 1}{4q - 4} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-1}{q - 1} \times \dfrac{4}{4} = \dfrac{-4}{4q - 4} $ Therefore $ p = \dfrac{-q + 1}{4q - 4} - \dfrac{-4}{4q - 4} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-q + 1 + 4 }{4q - 4} $ Distribute the negative sign: $p = \dfrac{-q + 1 + 4}{4q - 4}$ $p = \dfrac{-q + 5}{4q - 4}$